This research project is an investigator-initiated, randomized, double- blind, multicenter, clinical trial designed to test the primary null hypothese that warfarin therapy will not reduce the frequency of death or ischemic stroke recurrence by 30% compared with aspirin therapy. The trial will also test four secondary null hypotheses, not by sample size criteria, that the rate of death and recurrent stroke with warefarin will not be 50% lower in one year compared with aspirin therapy; there will be no differences between the two therapies in the frequency of recurrence by stroke severity or subtype, race or sex, nor by the initial CT scan lesion size and location for infarct, and the rate of complications will not differ. After thorough search for the cause of stroke, seeking image evidence of the site and size of the infarct and laboratory evidence in support of its cause, eligible patients wil be randomized to warfarin or aspirin using a double dummy design. Study drugs will be initiated within 30 days after stroke and treatment continued for at least two years. The patients will be followed monthly by phone and quarterly in person to regulate the hematologic effects of medication, detect the primary endpoints of death and symptomatic stroke recurrence, and complications of therapy. Transient ischemic attacks and myocardial infarction will be recorded but treated a secondary events. To maintain blinding, the blood samples will be sent to a central facility (MetPath) for determination of the prothrombin time and INRs. These results will be sent from MetPath to the Data Monitoring Center (DMC) and there entered into the patients's electronic record. After entry, a computer program will compare the values against the active treatment arm. The prothrombin time and INR results made available to the local investigator in charge of the given patient will be as reported from MetPath for those patients whose active study medication is warfarin but may be falsified for those whose active study medication is aspirin. An emergency notification system will be included to help maintain patient safety. The only person unblinded as to treatment assignment will be the prinicpal investigator statistician at the Data Mangement Center; all other pariticpants will be blinded.